Non-emptiness of moduli spaces of coherent systems
Abstract
Description
Let X be a general smooth projective algebraic curve of genus g>1. We prove that the moduli space G(α:n,d,k) of $α$-stable coherent systems of type (n,d,k) over X is empty if k>n and the Brill-Noether number is negative. Moreover, if the Brill-Noether number is positive and <g and for some $α>0$, G(α:n,d,k) is non-empty G(α:n,d,k) is non-empty for all $α>0$ and G(α:n,d,k)= G(α':n,d,k) for all $α,α'>0$ and the generic element is generated.
Revised version. To appear in Internat. J. Math 22 pages, AMS-Tex
Revised version. To appear in Internat. J. Math 22 pages, AMS-Tex